A composite function can be written as $w\bigl(u(x)\bigr)$, where $u$ and $w$ are basic functions. Is $g(x)=\log(6x^2-11)$ a composite function? If so, what are $u$ and $w$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $g$ is composite. $u(x)=\log(x)$ and $w(x)=6x^2-11$. (Choice B) B $g$ is composite. $u(x)=6x^2-11$ and $w(x)=\log(x)$. (Choice C) C $g$ is not a composite function.
Explanation: Composite and combined functions A composite function is where we make the output from one function, in this case $u$, the input for another function, in this case $w$. We can also combine functions using arithmetic operations, but such a combination is not considered a composite function. The inner function The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function. Here, we have $6x^2-11$ inside the parentheses. We evaluate this polynomial first, so $u(x)=6x^2-11$ is the inner function. The outer function Then we take the logarithm of the entire output of $u$. So $w(x)=\log(x)$ is the outer function. Answer $g$ is composite. $u(x)=6x^2-11$ and $w(x)=\log(x)$. Note that there are other valid ways to decompose $g$, especially into more complicated functions.